INDUMAT (Quiz 3)

Question 1

If |g’(x)| -> 1, convergence is _______.

Answer 1

Slow

Question 2

If |g’(x)| < 1, _________________.

Answer 2

There will be convergence.

Question 3

If |g’(x)| > 1, _________________.

Answer 3

There will be no convergence meaning divergence exists.

Question 4

Derivative of ln (u)

Answer 4

u’ / u

Question 5

Necessary and Sufficient Conditions for Local Minima (Theorem 1)

Answer 5

1. Equate first derivative to zero
2. Get the extreme points
3. Plug in the extreme points to the second derivative
4. If the value is greater than 0, it is a minima.

Question 6

Necessary and Sufficient Conditions for Local Maxima (Theorem 2)

Answer 6

1. Equate first derivative to zero
2. Get the extreme points
3. Plug in the extreme points to the second derivative
4. If the value is less than 0, it is a maxima.

Question 7

In Single Variable Unconstrained Optimization, suppose at a point x, the first derivative is zero, and the first non-zero higher-order derivative occurs at the nth derivative. If n is _____, then x is a point of inflection.

Answer 7

Odd

Question 8

In Single Variable Unconstrained Optimization, suppose at a point x, the first derivative is zero, and the first non-zero higher-order derivative occurs at the nth derivative. If n is _____, then x is a local minima if the derivative is _________ .

Answer 8

Even; Positive

Question 9

In Single Variable Unconstrained Optimization, suppose at a point x, the first derivative is zero, and the first non-zero higher-order derivative occurs at the nth derivative. If n is _____, then x is a local maxima if the derivative is _________ .

Answer 9

Even; Negative

Question 10

Another term for an inflection point

Answer 10

Saddle Point

Question 11

Another term for stationary point

Answer 11

Critical Point

Question 12

Convex Graph

Answer 12

U

Question 13

Concave Graph

Answer 13

∩

Question 14

Both Concave and Convex

Answer 14

\ or / (Linear Line)

Question 15

Steps for MOSS

Answer 15

1. Isolate all possible x then make into g(x)
2. Get the derivative and find which x would have the smallest value ( such that its < 1 ).
3. Using the acquired x, initialize with x0 at k=0
4. Substitute value and repeat process until error value is less than tolerable error.

Question 16

In constrained optimization, if the problem is asking to minimize, the constraints must be _____________ .

Answer 16

Equated to 0 such that g(x) is equal to 0.